On the smoothness of Hölder doubling measures

D. Preiss; X. Tolsa; T. Toro

doi:https://doi.org/10.1007/s00526-008-0208-z

On the smoothness of Hölder doubling measures

D. Preiss, X. Tolsa, T. Toro

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

16 Citations (Scopus)

Abstract

It is known that in low dimensions supports of Hölder doubling measures are C 1,β manifolds. In higher dimensions singularities may occur. We provide a full description of such supports by showing that they are C 1,β manifolds away from a closed set of measure zero and that at singular points they are uniformly far from being flat at every scale. © 2008 Springer-Verlag.

Original language	English
Pages (from-to)	339-363
Journal	Calculus of Variations and Partial Differential Equations
Volume	35
DOIs	https://doi.org/10.1007/s00526-008-0208-z
Publication status	Published - 1 Jul 2009

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title = "On the smoothness of H{\"o}lder doubling measures",

abstract = "It is known that in low dimensions supports of H{\"o}lder doubling measures are C 1,β manifolds. In higher dimensions singularities may occur. We provide a full description of such supports by showing that they are C 1,β manifolds away from a closed set of measure zero and that at singular points they are uniformly far from being flat at every scale. {\textcopyright} 2008 Springer-Verlag.",

author = "D. Preiss and X. Tolsa and T. Toro",

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doi = "https://doi.org/10.1007/s00526-008-0208-z",

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T1 - On the smoothness of Hölder doubling measures

AU - Preiss, D.

AU - Tolsa, X.

AU - Toro, T.

PY - 2009/7/1

Y1 - 2009/7/1

N2 - It is known that in low dimensions supports of Hölder doubling measures are C 1,β manifolds. In higher dimensions singularities may occur. We provide a full description of such supports by showing that they are C 1,β manifolds away from a closed set of measure zero and that at singular points they are uniformly far from being flat at every scale. © 2008 Springer-Verlag.

AB - It is known that in low dimensions supports of Hölder doubling measures are C 1,β manifolds. In higher dimensions singularities may occur. We provide a full description of such supports by showing that they are C 1,β manifolds away from a closed set of measure zero and that at singular points they are uniformly far from being flat at every scale. © 2008 Springer-Verlag.

U2 - https://doi.org/10.1007/s00526-008-0208-z

DO - https://doi.org/10.1007/s00526-008-0208-z

M3 - Article

VL - 35

SP - 339

EP - 363

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

SN - 0944-2669

ER -